Motion controlling

ABSTRACT

Motion controlling includes a combining network having an acceleration input for receiving an acceleration signal representative of acceleration of a movable element and a position input for receiving a position signal representative of position of the movable element and an output for providing an inferred position signal representative of an inferred position of the movable element. The network includes a first signal processor for processing the acceleration signal to provide modified acceleration signal, a second signal processor for processing the position signal to provide a modified position signal and a combiner for combining the modified acceleration signal with the modified position signal to provide the inferred position signal.

CLAIM OF PRIORITY

This application claims priority under 35 USC § 119(e) to U.S. patentapplication Ser. No. 08/677,380, filed on Jul. 5, 1996, the entirecontents of which are hereby incorporated by reference.

TECHNICAL FIELD

The invention relates to servo systems, and more particularly to motioncontrolling and position sensing, and still more particularly to motioncontrol systems employing accelerometers.

BACKGROUND OF THE INVENTION

For background, reference is made to Dorf and Bishop, Modern ControlSystems, Seventh Edition, 1995, Addison-Wesley Publishing Company, ISBN0-201-50174-0, especially to Chapters 2, 4 and 8.

It is an important object of the invention to provide improved motioncontrolling.

BRIEF SUMMARY OF THE INVENTION

In one aspect of the invention, a combining network in a closed loopfeedback control system combines an acceleration signal (representing anacceleration of a movable element) and a position signal (representing aposition of the movable element) to produce an inferred position signal(representing an inferred position of the movable element). Thecombining network includes a first signal processor for processing theacceleration signal to provide a processed acceleration signal and acombiner for combining the processed acceleration signal with theposition signal to provide the inferred position signal.

In another aspect of the invention, in a closed loop feedback controlsystem, a method for combining an acceleration signal and a measuredposition signal to provide an inferred position signal includes low-passfiltering the acceleration signal to provide a filtered accelerationsignal and combining the filtered acceleration signal with the measuredposition signal to provide the inferred position signal.

In another aspect of the invention, apparatus for detecting positionincludes an accelerometer for providing an acceleration signalrepresentative of acceleration, a position sensor for providing aposition signal representative of position, a first processor forprocessing the acceleration signal to provide a modified accelerationsignal, a combiner for combining the acceleration signal and theposition signal to yield an inferred position signal representative ofinferred position.

In another aspect of the invention, a motion control apparatus includesa movable element, an input for receiving a signal representative of adesired position of the movable element, a position sensor for providinga position signal representative of the position of the movable element,an accelerometer for providing an acceleration signal representative ofthe acceleration of the movable element, and a combining network forcombining the position signal and the acceleration signal for providingan inferred signal representative of an inferred position for themovable element. The combining network includes a first processor forprocessing the acceleration signal to provide a processed accelerationsignal, a combiner for combining the processed acceleration signal andthe position signal to provide the inferred position signal, a summerfor comparing the inferred position signal with the desired positionsignal to provide a control signal, and a mover responsive to thecontrol signal for moving the movable element to reduce the differencebetween the inferred position and the desired position.

In another aspect of the invention, a circuit for combining theacceleration signal and the position signal to provide the inferredsignal includes an input for the acceleration signal; a first resistorhaving an input connected to the acceleration signal input; a firstcapacitor having an input connected to the output of the first resistorand having a grounded output; a second resistor having an inputconnected to the input of the first capacitor and the output of thefirst resistor; an input for the position signal; a third resistorhaving an input connected to the input for the position signal; a secondcapacitor having an input and an output, the input of the secondcapacitor connected to the output of the third resistor and the outputof the second capacitor being grounded; a fourth resistor having aninput connected to the input of the second capacitor and the output ofthe third resistor; an operational amplifier having an inverting inputconnected to the output of the second resistor and the output of thefourth resistor, the noninverting input of the operational amplifierbeing grounded; a fifth resistor having an input coupled to the outputof the second resistor and the output of the fourth resistor; an outputfor the inferred signal coupled to the output of the fifth resistor andto the output of the operational amplifier; and a fifth capacitor,connected in parallel with the fifth resistor.

In another aspect of the invention, a position detection apparatusincludes an accelerometer for providing an acceleration signalrepresentative of acceleration of a movable element, a combining networkhaving an acceleration input for receiving the acceleration signal, aposition input for receiving a position signal representative ofposition of the movable element, and an output for providing an inferredposition signal representative of an inferred position of the movableelement. The network includes a first signal processor for processingthe acceleration signal to provide a modified acceleration signal. Thefirst signal processor includes a low-pass filter, a second signalprocessor for processing the position signal to provide a modifiedposition signal, and a combiner for additively combining the modifiedacceleration signal with the modified position signal to provide theinferred position signal.

In another aspect of the invention, a position detection method forprocessing an acceleration signal and a measured position signalrepresentative of acceleration and position, respectively, of a movableelement to provide an inferred position signal includes low-passfiltering the acceleration signal and additively combining the low-passfiltered acceleration signal with the position signal to provide theinferred position signal.

In another aspect of the invention, a closed loop motion controlapparatus includes a movable element having a position, an accelerometerfor providing an acceleration signal representative of acceleration ofthe movable element, a combining element, for combining a referenceposition signal and an inferred position signal to provide an errorsignal, a controller, for providing a control signal responsive to theerror signal, and an actuator, for applying a force, responsive to thecontrol signal, to the movable element to change the position of themovable element. The force results in the acceleration of the movableelement. The apparatus further includes a feedback loop, for providingthe inferred position signal. The feedback loop includes a combiningnetwork for providing the inferred position signal. The combiningnetwork includes an acceleration input for receiving the accelerationsignal, a position input for receiving a position signal representativeof position of the movable element, and an output for providing aninferred position signal representative of an inferred position of themovable element. The network includes a first signal processor forprocessing the acceleration signal to provide a modified accelerationsignal. The first signal processor includes a low-pass filter, a secondsignal processor for processing the position signal to provide amodified position signal, and a combiner for additively combining themodified acceleration signal with the modified position signal toprovide the inferred position signal.

In still another aspect of the invention, an open loop positiondetection apparatus includes an accelerometer for providing anacceleration signal representative of acceleration of a movable element,a combining network having an acceleration input for receiving theacceleration signal, a position input for receiving a position signalrepresentative of position of the movable element, and an output forproviding an inferred position signal representative of an inferredposition of the movable element. The network includes a first signalprocessor for processing the acceleration signal to provide a modifiedacceleration signal, the first signal processor comprising a low-passfilter, a second signal processor for processing the position signal toprovide a modified position signal, and a combiner for additivelycombining the modified acceleration.

A motion control system according to the invention is advantageous,because it greatly enhances the signal to noise ratio in providing theposition signal, thereby enabling more accurate control of position inthe presence of noise. Furthermore, in digital control systems, a motioncontrol system according to the invention, is free of an anti-aliasingfilter and consequently allows the faster sampling rates and greaterbandwidth; because at high frequencies, the invention uses therelatively high signal-to-noise ratio acceleration signal for providingthe inferred position signal; and because at high frequencies therelatively low signal-to-noise ratio position signal is heavilyfiltered, thereby significantly attenuating noise.

Other features, objects, and advantages will become apparent from thefollowing detailed description, which refers to the following drawingsin which:

BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWING

FIG. 1 is a block diagram of a motion control system according to theinvention;

FIG. 2 is a block diagram of the motion control system of FIG. 1, withtransfer functions of various elements;

FIG. 3 is a block diagram of an embodiment of the combining networkportion of FIGS. 1 and 2;

FIG. 4 is a Bode plot of the effects on position and accelerationsignals of the elements of the block diagram of FIG. 3;

FIG. 5 is a block diagram of an alternate embodiment of the combiningnetwork portion of FIG. 2;

FIG. 6 is a block diagram of a simplified version of the combiningnetwork of FIG. 5;

FIG. 7 is a schematic diagram of a circuit which implements elements ofthe combining network of FIG. 6;

FIG. 8 is a Bode plot showing the effects of the combining network ofFIG. 6;

FIG. 9 a is a Bode plot of gain in dB vs. log frequency for some valuesof a defined ratio α;

FIG. 9 b is a Bode plot of phase in degrees vs. log frequency for somevalue of the a defined ratio α;

FIG. 10 is a block diagram of an alternate embodiment of the combiningnetwork of FIG. 2;

FIG. 11 is a pole/zero diagram for the defined transfer function A(s)for various values of a defined ratio α;

FIG. 12 is a circuit which implements elements of the block diagram ofFIG. 10;

FIGS. 13 and 14 are block diagrams of another motion control systemaccording to the invention;

FIGS. 15 and 16 are block diagrams of an open loop system incorporatingthe invention; and

FIGS. 17 and 18 are block diagrams of another open loop systemincorporating the invention.

DETAILED DESCRIPTION

With reference now to the drawings and more particularly to FIG. 1,there is shown a block diagram of a position control system according tothe invention. Corresponding elements are identified by the samereference symbols throughout the drawings. Summer 16 has an input 8 forreceiving a reference position signal x_(ref) and an input 10 forreceiving an inferred position signal x_(inferred). Summer 16 is coupledto a controller 20, which is in turn coupled to an actuator 22. Actuator22 is mechanically coupled to a movable element 26 to move the element.Movable element 26 is coupled to an accelerometer 28 and to a positionsensor 30. Accelerometer 28 and position sensor 30 are coupled to acombining network 32, which is in turn coupled to input 10 of summer 16.

Summer 16, actuator 22, movable element 26, and position sensor 30 maybe conventional devices, and controller 20 may be a conventional PID(proportional integral derivative) controller. The invention is usefulin a wide variety of applications (including, but not limited to, thosementioned above) and with other components (including, but not limitedto, other types of controllers) to detect or control the position ofdevices.

Referring now to FIG. 2, there is shown the position control system ofFIG. 1 with blocks designating transfer functions associated with someelements. Summer 16 provides an error signal x_(error) representative ofthe difference between the signals x_(ref) and x_(inferred) (that issums [x_(ref) and −x_(inferred)] indicated by the “+” at summer input 8and the “−” at summer input 10 or sums [−x_(ref) and x_(inferred)]).Controller 20 responds to the error signal by furnishing a controlsignal to actuator 22 for reducing the error signal. Actuator 22 appliesa force F to movable element 26, resulting in an acceleration (a or, thesecond derivative of the position x) according to the Newtonian formulaF=ma. Accelerometer 28 (shown in FIG. 2 as a summer for reasons thatwill be explained below) provides an acceleration signal representativeof the acceleration. Position sensor 30 measures the position x, whichis the second integral of the acceleration, receives a position signalrepresentative of the second integral of the acceleration. Summers 31and 28 receive noise n₁ and n₂ added to the position signal x andacceleration measurement signal, respectively. Combining circuit 32accepts as input the acceleration signal with noise n₂ fromaccelerometer 28 and the position signal with noise n₁ from positionsensor 30 provides an inferred position signal x_(inferred) which is fedback to summer 16.

Referring now to FIG. 3, there is shown combining network 3 in moredetail. The combining network which has at least two inputs selectivelyweighs the inputs based on frequency bands, and combines the weightedinputs to provide the inferred acceleration signal. In the embodiment ofFIG. 2, the combining network has as one input an acceleration signal,representative of the acceleration of a movable element, as a secondinput a position, representative of position of the movable element, andas an output a signal of an inferred position x_(inferred). A “crossoverfrequency” as used herein, refers to a predetermined frequency at whichtwo inputs to combining network are weighted relatively equally.

Still referring to FIG. 3, the output of accelerometer 28 (whichincludes the acceleration and noise n₂), is modified by a number ofmodifiers, which may include a high pass filter 31 and a scaler 42. Thequantities α and ω₀ defining the scaling factor are described below. Theoutput of scaler 42 is low pass filtered by low pass filter 44 which hasa break frequency ω₁ cascaded with a second low-pass filter 46 which hasa break frequency ω₂ to yield a modified accelerometer output signal(+n₂)_(modified).

The output of the position sensor 30, which includes the positionmeasurement signal x and noise n₁, is filtered by cascaded low-passfilters 48 and 49 with break frequencies of ω₂, to yield a modifiedposition sensor output signal (x+n₁)_(modifed). The modifiedaccelerometer output signal and the modified position sensor outputsignal are combined by combiner 52 to yield an output. The frequenciesω₁ and ω₂ are frequencies with the relationship ω₁ω₂=ω₀ ² (where ω₀ isthe crossover frequency, that is, a predetermined frequency at which theinputs from the accelerometer and the position sensor are weightedapproximately equally by the combining network) and α is defined as thequantity ω₂/ω₁

Referring to FIG. 4, there is a Bode plot showing the effects on thesignals of the elements of the block diagram of FIG. 3. The curves ofFIG. 4 represent the normalized output of the various elements of FIG. 3(in the form of log (V_(out)/V_(in))) as a function of frequency. Curve58 represents a signal representing the actual position. Curve 58-58 a(assuming for the purpose of this explanation, a “white noise” model)represents the modified position signal. At low frequencies, the signalto noise ratio is high, and the position signal accurately representsthe actual position. However, at high frequencies, at when the positionsignal becomes smaller but the noise does not, the signal to noise ratiois smaller, and the position signal diverges from accuratelyrepresenting the actual position. The position sensor signal 58 a athigh frequencies (such as ω_(u)) begins to diverge from the actualposition signal 58. Low pass filters 48 and 49 modify the positionsignal so that curve 58-58 b represent the output of the second of thelow pass filters 48. At frequencies below ω₂, low pass filters 48 and 49pass the signal from position sensor 30. However, the cascaded low passfilters 48 and 49 sharply attenuate spectral components above ω₂.

Curve 62 represents the acceleration signal essentially constant belowω₁. Optional high pass filter 31 significantly attenuates spectralcomponents above ω_(a) and has virtually no effect at frequencies in therange of ω₀, ω₁ and ω₂. Low pass filters 44 and 46 having breakfrequencies at ω₁ and ω₂, respectively, decrease the slope of curve 62to match that of curve 58 above ω₂. Effectively, the two low passfilters double integrate the acceleration signal to yield a positionsignal.

Curve 64 represents the output of signal combiner 52. At lowfrequencies, the modified output from position sensor 30 represented bycurve 58-58 b is of greater magnitude than the modified outputaccelerometer 28, so the output of summer 52 approximates the modifiedoutput 58-58 b of position sensor. Therefore, at low frequencies, thevalue can be used for the inferred position x_(inferred) in the controlsystem of FIGS. 1 and 2.

At high frequencies, the modified output represented by curve 62 fromaccelerometer 28 is of greater magnitude than the modified outputrepresented by curve 58-58B from position sensor 30, so the outputrepresented by curve 64 of combiner 52 approximates the modified outputrepresented by curve 62 of accelerometer 28. FIG. 4 shows that theoutput represented by curve 64 of combiner 52 varies from the actualposition signal curve 58 in the region between ω₀ and ω₂.

Referring to FIG. 5, there is shown combining network 32″ which is thecombining network 32′ of FIG. 3 with additional signal processors tocorrect for the effect of the different slope of line 62 in the regionbetween ω₀ and ω₂. Signal processor 54, which has a transfercharacteristic with a pole at ω₀ and signal processor 56 has a transfercharacteristic with a zero at ω₂ process the output {overscore (x)} ofcombiner 52 to produce a modified inferred position signal {tilde over(x)}. The product of the transfer characteristic of signal processor 56and those of low-pass filters 46 and 49 is unity so these signalprocessors may be omitted from the block diagram of FIG. 5 to form theequivalent block diagram of FIG. 6.

Referring to FIG. 6, combining network 32′″ provides an output signalthat can be expressed as:$\overset{\sim}{x} = {{\left( \frac{\omega_{0}\omega_{2}}{\left( {s + \omega_{0}} \right)\left( {s + \omega_{2}} \right)} \right)x} + {\left( \frac{\frac{\sqrt{a}}{\omega_{0}^{2}}*\omega_{0}\omega_{1}}{\left( {s + \omega_{0}} \right)\left( {s + \omega_{1}} \right)} \right)\overset{¨}{x}} + {\left( \frac{\omega_{0}\omega_{2}}{\left( {s + \omega_{0}} \right)\left( {s + \omega_{2}} \right)} \right)n_{1}} + {\left( \frac{1}{\left( {s + \omega_{0}} \right)\left( {s + \omega_{1}} \right)} \right)n_{2}}}$

-   -   which reduces to        $\overset{\sim}{x} = {{\left( \frac{s_{2} + {\left( {\sqrt{\alpha} - 1} \right)\omega_{0}s} + \omega_{0}^{2}}{s^{2} + {\left( {\sqrt{\alpha} + \left( {1/\sqrt{\alpha}} \right)} \right)\omega_{0}s} + \omega_{0}^{2}} \right)x} + {\left( \frac{\omega_{0}\omega_{2}}{\left( {s + \omega_{0}} \right)\left( {s + \omega_{2}} \right)} \right)n_{1}} + {\left( \frac{1}{\left( {s + \omega_{0}} \right)\left( {s + \omega_{1}} \right)} \right)n_{2}}}$

Since the break frequency ω_(a) of the high pass filter 31 issignificantly lower than the crossover frequency ω₀ or frequencies ω₁and ω₂, its effect on the signal is negligible and may be neglected. Forα>>1, the value of the coefficient$\left( \frac{s^{2} + {\left( {\sqrt{\alpha} - 1} \right)\omega_{0}s} + \omega_{0}^{2}}{s^{2} + {\left( {\sqrt{\alpha} + \left( {1/\sqrt{\alpha}} \right)} \right)\omega_{0}s} + \omega_{0}^{2}} \right)$of the position signal x, A(s) hereafter, is approximately 1. Thecascaded low-pass filters significantly attenuate the two noise terms n₁and n₂ integrates the output signal from accelerometer 28 to provide avelocity signal representative of the velocity of movable element 26 onterminal 53.

Referring to FIG. 7, there is shown a schematic diagram of a circuitembodying the combining network of FIG. 6. Inputs 68 and 69 areconnected to the outputs of accelerometer 28 and position sensor 30,respectively. Low pass filters 44 and 48 of FIG. 6 correspond to firstand second resistor and capacitor pairs 82 and 84, respectively, andsummer 52, signal processor 42 and low pass filter 54 of FIG. 6 are incircuit 86, which includes operational amplifier 87, capacitor 89 andresistor 91 connected in parallel. High pass filter 31 is conventionaland not shown in FIG. 7.

Referring to FIG. 8, there is shown a Bode plot with curve 64representing the output signal (see also FIG. 4) of a combining networkas shown in FIG. 3, a curve 58 of a signal representing the actualposition, and output signal 66 of a combining network as shown in FIG. 6(normalized) as a function of frequency. Curve 64 is a closerepresentation of the actual position, deviating slightly in the regionof frequencies near the crossover frequency ω₀.

Referring to FIG. 9 a, there is shown a Bode plot of gain in dB for thetransfer function A(s) for various values of α, normalized to afrequency of 1 radian/sec. At higher values of α, the gain of thetransfer function A(s) approaches zero dB (indicating that the value ofA(s) approaches 1 as was noted above).

Referring to FIG. 9 b, there is shown a graph of phase in degrees as afunction of frequency on a logarithmic scale for the transfer functionA(s) for the same values of α. The phase shift at higher values of αapproaches zero. The graphical representation of FIGS. 8, 9 a and 9 bshow that for large values of α, the output of the combining network ofFIG. 6 is a close representation of the actual position. The combiningnetwork of FIG. 6 is especially useful in the position control system ofFIGS. 1 and 2, with the output signal of FIG. 6 used for the signalx_(infrerred) of FIGS. 1 and 2.

Referring to FIG. 10, there is shown a block diagram of a combiningnetwork 32″″ which yields a closer representation of actual position inthe region near the crossover frequency ω₀. The network of FIG. 10includes the elements of FIG. 6, plus a reconstruction filter 74.Reconstruction filter 74 cancels the effect of the transfer functionA(s) and therefore yields as an output, which is virtually an exactrepresentation of the actual position, and the combining network of FIG.10 can be used in the position control system of FIGS. 1 and 2 with theoutput signal used for the signal x_(inferred) in FIGS. 1 and 2.

Referring to FIG. 11, there is shown a pole/zero diagram for thecoefficient A(s) for various values of α. Applying α≧9, quadraticformula for all α>9, the singularities are real, and therefore, with theteachings of this disclosure, the reconstruction filter can beimplemented with simple passive components. For values of α<9, the polesof the reconstruction filter 74 can be implemented actively withresistors and capacitors or passively with inductors and capacitors.

Referring to FIG. 12, there is shown a circuit embodying the network ofFIG. 10. The resistor capacitor pairs (82 and 84) and the circuit 86correspond to the similarly identified circuits of FIG. 7. Thereconstruction filter circuit 88 corresponds to reconstruction filter 74of FIG. 10. The output at terminal 76 is a signal representing the valueof x_(inferred) of FIG. 1, with significantly attenuated noise, and withthe measured value that is virtually an exact representation of theactual position of x.

Referring to FIGS. 13 and 14, there is shown a block diagram of anothermotion control system according to the invention. FIGS. 13 and 14include the elements of FIG. 1 and FIG. 2, respectively, and in additioninclude some additional elements. FIG. 13 includes reference elementaccelerometer 128 and acceleration combiner 129. Reference elementaccelerometer 128 provides an acceleration signal representative of theacceleration of a reference element. One input of acceleration combiner129 is additively coupled to the output of accelerometer 28 and a secondinput of acceleration combiner 129 is subtractively coupled to referenceelement accelerometer 129. The output of acceleration combiner 129 iscoupled to input of combining network 32.

Referring to FIG. 14, summer 129 differentially combines accelerationsignal from accelerometer 28 and reference acceleration signal fromreference element accelerometer 128. Summer 129 receives noise n₂ thatis a part of acceleration signal and reference acceleration signal.

In FIGS. 13 and 14, combining network 32 may take the forms of theelement 32′ of FIG. 3, element 32″ of FIG. 5, element 32′″ of FIG. 6, orelement 32″″ of FIG. 10, and can be implemented by the circuits of FIGS.7 and 12.

An implementation of the invention according to FIGS. 13 and 14 isuseful for a feedback control system in which a reference element cannotbe assumed to be an inertial ground.

A first practical example of the implementation of FIGS. 13 and 14 is amanufacturing operation in which a jig has an element that is movablewith respect to a fixture, and in which the jig is portable so that itmoves along an assembly line. In such an implementation, referenceelement accelerometer 128 could measure the acceleration of the jig sothat the position calculated by the combining network represents anaccurate position of the movable element relative to the jig, and isunaffected by the movement of the jig.

A second practical example is a motion control system in which theactuator exerts high force but which requires a high degree ofpositional accuracy. In such an implementation, reference elementaccelerometer 128 may measure the acceleration of the machine itself sothat the machine does not need to be structurally rigid, and so that themachine can be mounted in such a manner (such as on shock absorbingmounts) that the machine does not transmit vibration to the element towhich the machine is mounted.

A third practical example is an active vehicle suspension which operatesto control or minimize the vertical position and acceleration of a cargoor passenger compartment, such as the vehicle suspension systemdescribed in co-pending U.S. patent application Ser. No. 09/535,849.

Accelerometer 28 could measure the acceleration of the passenger orcargo compartment, and reference element accelerometer could measure theacceleration of the wheel or ground engaging device. Such animplementation could allow for a more accurate calculation and executionof a trajectory plan and better operation of the active vehiclesuspension.

Referring to FIGS. 15 and 16, there is shown an open loop systemincorporating the invention. In FIG. 15, an accelerometer 28 and aposition sensor 30 are coupled to combining network 32. The combiningnetwork 32 outputs a signal representative of position at outputterminal 102.

In FIG. 16, accelerometer 28 and position sensor 30 are represented assummers which receive noise n₂ and n₁ in addition to the signalrepresentative of acceleration {umlaut over (x)} and the signalrepresentative of position x, respectively. Combining network 32 maytake the forms of the element 32′ of FIG. 3, element 32″ of FIG. 5,element 32′″ of FIG. 6, or element 32“ ” of FIG. 10 and can beimplemented by the circuits of FIGS. 7 and 12. The output x_(inferred)could represent x as noted in the discussion of FIG. 10.

The implementation of FIGS. 15 and 16 is useful in position detectorsfor data acquisition situations in which feedback is not required.Examples may include instrumentation, for example an altimeter in whichthe position is derived from pressure sensing, and the accelerationrepresents vertical acceleration. Another example may include mobile andhigh speed tracking, profiling, or surveying equipment, in which theposition detection or measurement device is supplemented by anaccelerometer measuring the acceleration of the position detection andmeasurement device.

Referring to FIGS. 17 and 18, there is shown an open loop systemincorporating the invention and additionally including position sensor30, reference element accelerometer 128 and acceleration combiner 129similar to the like-numbered elements of FIGS. 13 and 14. In FIGS. 17and 18, combining network 32 may take the forms of the element 32′ ofFIG. 3, element 32″ of FIG. 5, element 32′″ of FIG. 6, or element 32“ ”of FIG. 10, and can be implemented by the circuits of FIGS. 7 and 12.

An implementation according to FIGS. 17 and 18 is useful in positiondetectors in which a reference element cannot be assumed to be aninertial ground and which do not require feedback. Practical examplesmay include instrumentation systems similar to the examples stated abovein the discussion of FIGS. 13 and 14, but which display or record theinferred position as output data rather than using the inferred positionin a feedback loop.

Other embodiments are within the claims.

1. Position detection apparatus, comprising: an accelerometer forproviding an acceleration signal representative of acceleration of amovable element, a combining network having an acceleration input forreceiving said acceleration signal, a position input for receiving aposition signal representative of position of said movable element, andan output for providing an inferred position signal representative of aninferred position of said movable element, said network including afirst signal processor for processing said acceleration signal toprovide a modified acceleration signal, said first signal processorcomprising a low-pass filter, a second signal processor for processingsaid position signal to provide a modified position signal, and acombiner for additively combining said modified acceleration signal withsaid modified position signal to provide said inferred position signal.2. Position detection apparatus in accordance with claim 1, furthercomprising: a second accelerometer, for providing a reference elementsignal representative of acceleration of a reference element; adifferential acceleration measuring element, comprising a firstacceleration input for receiving said movable element accelerationsignal, a second acceleration input for receiving said reference elementacceleration signal, and an output for providing a differential outputsignal representative of a differential acceleration of said movableacceleration signal and said reference element acceleration signal,wherein said combining network acceleration input is for receiving saiddifferential acceleration signal, and wherein said combining networkfirst signal processor is for processing said differential accelerationsignal to provide said modified acceleration signal.
 3. Positiondetection method for processing an acceleration signal and a measuredposition signal representative of acceleration and position,respectively, of a movable element to provide an inferred positionsignal comprising: low-pass filtering said acceleration signal; andadditively combining the low-pass filtered acceleration signal with saidposition signal to provide said inferred position signal.
 4. Positiondetection method in accordance with claim 3, wherein said accelerationsignal is a movable element signal representative of acceleration of amovable element, and wherein said method is further for processing areference element signal representative of acceleration of a referenceelement, said method further comprising: differentially combining saidmovable element acceleration signal and said reference elementacceleration signal to provide a differential acceleration signalrepresentative of differential acceleration of said movable element andsaid reference element; low pass filtering said differentialacceleration signal; and additively combining the low pass filteredacceleration signal with said position signal to provide said inferredposition signal.
 5. Closed loop motion control apparatus, comprising: amovable element having a position, an accelerometer for providing anacceleration signal representative of acceleration of said movableelement, a combining element, for combining a reference position signaland an inferred position signal to provide an error signal, acontroller, for providing a control signal responsive to said errorsignal, an actuator, for applying a force, responsive to said controlsignal, to said movable element to change said position, said forceresulting in said acceleration of said movable element, a feedback loop,for providing said inferred position signal, said feedback loopcomprising a combining network for providing said inferred positionsignal, said combining network including an acceleration input forreceiving said acceleration signal, a position input for receiving aposition signal representative of position of said movable element, andan output for providing an inferred position signal representative of aninferred position of said movable element, said network including afirst signal processor for processing said acceleration signal toprovide a modified acceleration signal, said first signal processorcomprising a low-pass filter, a second signal processor for processingsaid position signal to provide a modified position signal, and acombiner for additively combining said modified acceleration signal withsaid modified position signal to provide said inferred position signal.6. Closed loop motion control apparatus in accordance with claim 5,further comprising a reference element, a second accelerometer, forproviding a reference element acceleration signal representative ofacceleration of said reference element; a differential accelerationmeasuring element, comprising a first acceleration input for receivingsaid movable element acceleration signal, a second acceleration inputfor receiving said reference element acceleration signal, and an outputfor providing a differential output signal representative of adifferential acceleration of said movable acceleration signal and saidreference element acceleration signal, wherein said combining networkacceleration input is for receiving said differential accelerationsignal, and wherein said combining network first signal processor is forprocessing said differential acceleration signal to provide saidmodified acceleration signal.
 7. Open loop position detection apparatus,comprising: an accelerometer for providing an acceleration signalrepresentative of acceleration of a movable element, a combining networkhaving an acceleration input for receiving said acceleration signal, aposition input for receiving a position signal representative ofposition of said movable element, and an output for providing aninferred position signal representative of an inferred position of saidmovable element, said network including a first signal processor forprocessing said acceleration signal to provide a modified accelerationsignal, said first signal processor comprising a low-pass filter, asecond signal processor for processing said position signal to provide amodified position signal, and a combiner for additively combining saidmodified acceleration signal with said modified position signal toprovide said inferred position signal.
 8. Open loop position detectingapparatus in accordance with claim 7, further comprising a secondaccelerometer, for providing a reference element acceleration signalrepresentative of acceleration of a reference element; a differentialacceleration measuring element, comprising a first acceleration inputfor receiving said movable element acceleration signal, a secondacceleration input for receiving said reference element accelerationsignal, and an output for providing a differential output signalrepresentative of a differential acceleration of said movableacceleration signal and said reference element acceleration signal,wherein said combining network acceleration input is for receiving saiddifferential acceleration signal, and wherein said combining networkfirst signal processor is for processing said differential accelerationsignal to provide said modified acceleration signal.